No need to get into legalities when some simple communication can work wonders.
First, arm yourself with facts by going to your town's municipality to find out your rights and the rules that residents need to follow on trash collection days. With this information, politely and without being angry, go to your neighbor's house and state that you are entitled to put your trash cans curbside on trash collection days and expect to do so in order for your trash to be collected, like everyone else's.
My trash is also expected to be brought across the street to be collected. My road frontage is 50' wide. Across the street from my property is two driveways and a mail box. Our rules are that our trash bins have to be 4' from each other and all other objects for the mechanical arms to open, pick up the trash bin, empty the trash and set the bin down. I have no other choice but to put my trash bins across the street from my next door neighbor's house, essentially in what they deem "their" space for their trash cans on collection day.
I have had to, on numerous occasions, to move my neighbor's bins closer together so I have the space for my own bins. Once my neighbor "caught" me and was angry that I touched their trash bins. After I explained my side of the situation, they realized they were being irrational and unreasonable. SInce then, there have been no issues.
So, talk to your neighbor.